The equation 1/(x+2) + 1/(x-2) = 1 has two solutions. What is the sum of the solutions?

• A. 2
• B. 0
• C. 4
• D. -2

Answer: (A)

Combining the fractions turns a rational equation into a quadratic, which makes the relationship between the solutions simple to read off. Add the two fractions: (x−2 + x+2) divided by (x+2)(x−2) simplifies to 2x/(x^2−4). Setting this equal to 1 gives 2x/(x^2−4) = 1. Multiply both sides by x^2−4 (valid since x ≠ ±2 in the original equation): 2x = x^2 − 4, which rearranges to x^2 − 2x − 4 = 0. For this quadratic, the sum of the roots is −(−2)/1 = 2. You can also see the roots explicitly as x = 1 ± √5, both valid since neither equals ±2. Therefore, the sum of the solutions is 2.